where \(d(i,j)\)  denotes the local shortest-path distance between points associated with nodes \(i\)  and \(j\) , \(\nu \)  is a scalar, and \(\mathcal {N}(j)\)  is the set of neighbors of \(j\) . In order to analyze some of the geometric and topological properties of these graphs (e.g., patterns of connectivity), we can use spectral graph theory [1]}, and in particular, the normalized graph Laplacian \({L}={D}^{-1/2}{W}{D}^{-1/2}\) . Here \({D}\)  stands for the diagonal degree matrix whose elements verify \(D_{ii} = \sum _j W_{ij}\) .
